Heat exchanger tubes which are used in automobile radiators are typically manufactured in a tubing mill, the tube as it exits from the mill being cut to precise repeatable lengths, for example 21". Various machines have been developed for cutting the tubes to length and one such machine is shown in U.S. Pat. No. 3,292,472 issued Dec. 20, 1966. While the aforesaid patent could precisely cut tubes to repeatable lengths, the apparatus of said patent was limited to use with tube mills wherein the speed of the tube as it exited from a tube mill did not exceed 210' per minute. Recently tube cutting machines have been developed which can operate at higher tube speeds, one being shown in U.S. Pat. No. 4,462,290, issued July 31, 1984, and another being the McKenica model MHS-6 welded seam radiator tube cutoff machine. In each of these designs, the output shaft of a motor is connected to one end of a connecting rod with various cams, the other end of the connecting rod being connected through a pivot pin to a carriage. The cams cause the carriage to be moved at a linear speed equal to the speed of the tube to be cut during a limited portion of movement. However, it is desirable that tube cutoff machines operate at even higher tube speeds as the tube mills presently on the market can operate at higher speeds than the tube cutoff machines presently on the market.